About Buying Online
On the brand's website, https://coatsskin.com/, they link to their products they sell via their Amazon UK storefront. If you click on the "shop" link on the CoatsSkin site, it brings you to this page: https://coatsskin.com/collections/all. From there, if you click on a product, it brings you to that company's actual product on Amazon (as opposed to an imposter product).
Should you decide you want to try the product, go to the brand's website, and click their links to their products. It will bring you to the legitimate versions on Amazon. Provided you follow their links to their products, I don't think you have to worry on that particular front for these Coats products.
In general, when buying on Amazon, check out on the Amazon page who the seller is and who is shipping it (in UK, this is worded as "Dispatches from"). In the case of the Coats products, the seller is Coats Beauty and it dispatches from Amazon.
About Buying This Product Online
Coats is likely a new brand, just getting off the ground. If so, it's less overhead for them to use Amazon to distribute, than to set up their own system. And they probably haven't yet been able to get the product into stores.
The cleanser is currently unavailable: https://www.amazon.co.uk/Hydrating-Ceramides-Hyaluronic-Moisturise-Combination/dp/B0BHWQ5SK3?maas=maas_adg_A3F56A791E6BA16D8300615908693593_afap_abs&ref_=aa_maas
The toning milk is also currently unavailable: https://www.amazon.co.uk/Coats-Gentle-Hydrating-Toning-Milk/dp/B0BJ39DNJ7?maas=maas_adg_55F12980D55C4C681B63055BC180B431_afap_abs&ref_=aa_maas&tag=maas
The water face cream is unavailable, too: https://www.amazon.co.uk/Coats-Moisture-Moisturiser-Ceramides-Vitamin/dp/B0BJ3B4J89?maas=maas_adg_8BBE16B4FB887585E65AFA229091B619_afap_abs&ref_=aa_maas&tag=maas
Note, however, that the three products are available if you buy them as a suite: https://www.amazon.co.uk/dp/B0BRL915LQ?maas=maas_adg_755E8B6DFBA80E0C89005C7EB39ADC97_afap_abs&ref_=aa_
About This Brand's Business Approach
Bundling all three products for sale, but not selling each item separately is a marketing gimmick.
The company knows customers might be interested in one product to start, but if they bundle them, you have to pay for all three, to get the one you want. This isn't the hallmark of a scam, but in my opinion, it's a cynical way for a company to do business. It automatically makes me dislike them (and probably unfairly so on my part).
If your Product A is good, chances are I will check out your Products B and C on my own, provided they work for my skin type, with my sensitivities, and address one of my needs. The bundling, alone, would make me not buy the products, because I don't care to be bullied into buying three different products, when I just want to try one of them. I'm cranky like that, though.
NOTE: On the US version of Amazon, each product is available separately. Were I in UK, that would tick me off, even more.
Cleanser (US) Toning Milk (US) Water Cream Moisturizer (US)
About Dr. Charles MD's "Recommendation"
Please note that on the bottom of your screenshot, it says "Paid partnership."
Dr. Charles is doing a paid advertisement for this product, not an unbiased review.
Now, Dr. Charles may well think this is a great product, but he might also think it is just "good enough" to hawk in good conscience, or he may not have even tried it. I don't know. I'm not even familiar with his online presence, so I don't have a good feel for how meaningful this is. There are some doctors and influencers I trust, because they are so deliberate in which products they review, and make it a point to differentiate in obvious ways between their independent reviews, their free gift reviews, their paid endorsements, etc. I don't have a feel for how this man operates.
About the TikTok Buzz
It looks to me like Coats is putting a lot of effort into creating an online ad campaign that looks organically viral (but isn't), via TikTok. One of the tabs on the top of the company's homepage is "TikTok Trials."
There's nothing wrong with pre-fabricated "viral" online marketing, just learn to recognize it when you see it. It isn't like the whole internet just simultaneously discovered these products and felt the need to share them. Every video I've watched (tbh just a few, and just since I saw this post of yours) sounds to me like the influencer is reading off of a press release that accompanied a PR package of products.
About the Products
The products are probably fine, they might even be great, and you might even love them. Look over the ingredients in each one, to make sure they're something you'd want to put on your face. Think about whether you want to invest in three new products, when you are primarily interested in one.
And? If you try them out, go slowly. Patch test them, and don't incorporate all three into your routine in one go. Try one for a week or two, see if it agrees with you, then try the second one, etc. Then let us know what you think as someone who is not on TikTok's payroll.